Papastathopoulos, who will wear the No. 5 shirt, becomes new head coach Unai Emery's third signing after right-back Stephan Lichtsteiner arrived on a free transfer from Juventus and goalkeeper Bernd Leno joined from Bayer Leverkusen.
The Gunners have announced that the experienced defender has signed a "long-term contract" after joining for "an undisclosed fee".
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His two goals within four minutes proved to be very important as they survived the Argentines' scare in the later minutes of the game.
Sokratis becomes Arsenal's third signing of the summer.
The Greece worldwide also adds to the team's contingent of former Dortmund players, with Mislintat having already helped orchestrate the signings of Pierre-Emerick Aubameyang and Henrikh Mkhitaryan since arriving at Arsenal from the German club.
"Greek worldwide Sokratis Papastathopoulos has joined us on a long-term contract for an undisclosed fee", a statement on Arsenal's website read.
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Edinson Cavani gave Uruguay the lead after just six minutes of play, heading home a Luis Suarez cross. Uruguay advanced to a quarterfinal against France, which beat Argentina 4-3 earlier Saturday.
After his unveiling today, Sokratis sat down and spoke to Arsenal's in-house television station, where he revealed that - aside from the club's obvious appeal - exactly what attracted him to the Emirates.
"Arsenal is one of the three biggest clubs in the Premier League, it has a lot of fans, a very big history and I am very happy and for the next year I will be here to help the team".
"It's also very handsome how I come to a team and also have two players that I've been with for a lot of years, so I know them both very well and I'm very happy".
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Pressure will now be on Pompeo to make progress in negotiations with North Korea to turn the summit declaration into concrete action.